I would say your chances of getting 10 out of 15 right by blind guessing would be about a 1 or a 2 out of five. I would tell you to do a little educated guessing, using what you know or think you know, while choosing "C" when you have no clue, since that strategy does still work. The expected number of correct answers that you would get by randomly guessing by my estimation would be 5-8 max. If nothing else CRAM right before the exam!

There are 3003 ways in which you can get exactly 10 questions out of 15 right: 15!/(10!5!)=3003. The odds of getting any particular one of these permutations at random is very small: (.25^10)*(.75^5). Thus, the odds of getting any of the permutations making this combination (10/15) at random are the product of these two quantities ... which works out to about 0.06796%. There appears to be about a 91% chance you will get no more than 5 questions correct, guessing the answers at random. The number you are most likely to get right this way is either 3 or 4, and you have a 45% chance of doing that. This problem gave me an idea for a casino game. Up to six players may play at a table. An ordinary deck of playing cards is separated according to rank (all the Aces together, all the 2's together, etc.). One card will be pulled from each of the 13 groups. Before starting, each player bets he can guess what the suit of each card pulled will be. Individual players are paid according to how many they get right. Minimum number right for a win is 4, where the player is paid even money (1:1). The casino can maintain a huge edge and still have a very exciting payout schedule, topping out around 50,000,000:1 for getting all 13. The game includes the gambler's curse of intermittent reinforcement, meaning that each loss will only make many players more intense about the next possible win. High drama will attend nearly every flipped card. Side bets are also possible, e.g., players may bet on each individual flip as well as the entire series, being paid 2:1 for a win. Sounds like fun, eh? Yeah, for the casino, lol.